By using Uhlenbeck-Yau’s continuity method, we prove the existence of an approximate affine (σ,τ)-Hermite-Yang-Mills structure on affine (σ,τ)-semi-stable twisted quiver bundles R with a compact affine Gauduchon manifold as the base manifold. The obtained result can be viewed as an extension of classical results on quiver bundles.

Firstly, we used  geometric analysis methods to study the first nonzero eigenvalue of the weighted p-Laplace operator under the normalized or unnormalized weighted Yamabe flow,and obtained its evolution equations. Secondly, as applications, we prove that under the unnormalized weighted Yamabe flow, the eigenvalue λ_p,q(t)  strictly monotonically increases, while under the normalized weighted Yamabe flow, λ_p,q(t)e^ωt  strictly monotonically increases.

By using variational method, critical point theory and truncation techniques, we studied the multiplicity of periodic solutions for a class of nonlinear fractional Laplacian system. When the nonlinear term satisfies appropriate conditions, we prove that for any positive integer k>0, the system has k pairs of periodic solutions with period T.

We considered the blow-up properties of solutions to a class of fourth-order parabolic equations with Hessian terms by using the regularity theory of elliptic equations, Sobolev’s embedding inequalities and energy estimate methods. Firstly, we discussed the influence of weight functions and Hessian nonlinearity on the blow-up behavior of solutions.  Secondly, we  established differential inequalities for the square-integrable norms of the solutions, and qualitatively analyzed  several types of differential inequalities to give a lower bound estimate of the blow-up time and its qualitative relationship with the weight functions.

We considered the initial-boundary value problem for a class of variable-coefficient wave equations with logarithmic source terms and viscoelastic terms. Firstly, we discussed the influence of the logarithmic source terms and viscoelastic terms on the long-time dynamic behavior of solutions in inhomogeneous media. Secondly, by constructing a special type of multiplier and combining it with logarithmic Sobolev inequalities, we prove that the energy functional of the system decays exponentially when the initial energy satisfies 0<E(0)<d(d is the well depth).

We first used Sobolev inequalities and energy estimates to prove the global existence of solutions to the four-dimensional cubic complex Ginzburg-Landau equation. Then, we used the Gronwall lemma and Holder’s inequality to prove the existence of the absorption set of the equation and gave both the existence and compact connectedness of the maximal attractor of the equation.

We discussed the existence and stability of solutions for a class of nonlinear Caputo-type fractional q-difference equations with nonlocal integrals and generalized anti-periodic boundary conditions. Firstly, by using the Banach contraction mapping principle, we gave proof of the existence and uniqueness of solutions to the boundary value problem. Secondly, we gave Ulam stability results for this problem. Finally, the validity of the obtained results was verified through an example.

Let R be a ring, m and n be no-negative integers with m≤n. We prove that the triple (GFC_m,P_n,P^⊥_m∩GFC_n) is a hereditary Hovey triple in category GFC_n, the corresponding homotopy category is (GFC_m∩P^⊥_m)/(P_m∩P^⊥_m)=GFC/P, where P_n is the class of modules of projective dimension ≤n and GFC_n is the class of modules of Gorenstein FC projective dimension ≤n.

Firstly, we gave a relatively concise proof concerning the relationship between the length of subspace orbits and the exponent of subspace polynomials. Secondly,  by applying Frobenius shifts to subspaces and merging  cyclic subspace codes, we obtained cyclic subspace codes with a larger size of ((rn(q^N-1)/(q-1)) and a minimum distance of 2k-2. Finally, we gave an example of constructing a cyclic subspace code.

We discussed the general total coloring of the join graph P_m∨P_n that was vertex-distinguished by multisets by using the methods of 
proof by contradiction, explicit coloring construction, and  pre-assigned color set method, and determined general total chromatic number of its corresponding vertex-distinguished by multisets.

Aiming at the  rules acquisition for attribute-induced three-way property-oriented concept lattices, by defining weak consistency, we solved the problem of rules acquisition in general formal decision contexts and explored its  relationship with property-oriented  rules. Firstly, we  defined the attribute-induced three-way property-oriented weak consistency  and corresponding rules, and gave the relationship between attribute-induced three-way property-oriented weak consistency and property-oriented weak consistency, as well as the inclusion relationship between the two types of attribute rules. Secondly, we  demonstrated through examples that the obtained rules  using this method are more comprehensive and reasonable.

Based on the log-conformation representation (LCR), we gave two fully coupled numerical methods  for viscoelastic Oldroyd-B flow problems, and conducted a comparative study on two methods. The first method was to introduce the discrete elastic-viscous split-stress gradient (DEVSS-G) method into the momentum equation, which enhanced the ellipticity of the momentum equation and obtained the LCR-DEVSS-G stabilization scheme. The second method was to combine the streamline upwind Petrov-Galerkin (SUPG) method, we obtained  the LCR-SUPG stabilization scheme. Finally, the verification results of numerical examples of Poiseuille flow and flow around a circular cylinder show  that using LCR-DEVSS-G stabilization scheme to handle viscoelastic Oldroyd-B flow problems has  better convergence and higher computational efficiency.

Aiming at  the isotropy problem caused by the widespread use of cosine metrics in proxy-based deep metric learning methods, we  proposed a deep metric learning method that integrated Euclidean geometry and hyperbolic geometry. By introducing hyperbolic geometry with advantages in hierarchical modeling,  a local hyperbolic loss function was designed in hyperbolic space, and  the distribution prior of hyperbolic space was used to initialize proxy points reasonably. During training process, the local neighborhood proxy points corresponding to each sample were dynamically optimized, thereby effectively enhancing the inter-class discriminative ability of the model in local regions. Experimental results show that the proposed method exhibits significant performance improvements on multiple standard image retrieval datasets, thus validating the effectiveness of blending different geometric 
properties for enhancing discriminative performance in metric learning.

Aiming at the problems that the  knowledge graph completion method based on  Transformer as the backbone network, included parameter redundancy in feed-forward networks, difficulties in identifying tail entities under commonsense scenarios, and embedding biases in contrastive learning, we proposed an adapter-enhanced knowledge graph completion algorithm that 
integrated large language models with multi-positive sample contrastive learning. The algorithm reduced redundant features by introducing multi-head adapters in feed-forward network, and utilized  large language models to enhance commonsense reasoning ability. At the same time, it corrected embedding biases through  multi-positive sample contrastive learning. Experimental results 
show that, compared to the current state-of-the-art models, the algorithm improves MRR by 5.4% and 9.2% on WN18RR and FB15k-237 datasets, respectively, and by  3.6% and 6.7% in transductive and inductive settings  on the more complex Wikidata5M dataset,  respectively, and demonstrates superior generalization ability under low-resource and complex scenarios.

Aiming at the problems of large scale and high computational cost in existing high-accuracy object detection models,  it was difficult to deploy them widely in resource-limited  environments, we proposed a colaborative lightweight method  that integrated knowledge distillation, model quantization, and network pruning to construct an efficient  behavior detection model suitable for classroom scenarios. The method first achieved effective knowledge transfer from large to medium and small models through step-by-step distillation,  then combined structured pruning  to obtain a  lightweight  network equivalent to small-scale models, and further used  quantized feature distillation  to enhance feature expression ability of the model in  quantization-aware training.  Experimental results show  that the improved lightweight model has significantly higher detection accuracy than the original small  model  while  maintaining a small parameter size and  computational complexity. Its performance has steadily improved  on multiple classroom behavior datasets.

Aiming at the challenge of adaptive graph learning in unsupervised domains, we proposed a domain adaptive graph convolutional network based on data augmentation. The network first constructed a high-order neighborhood relationship matrix and adjacency matrix to jointly guide information propagation and learn more comprehensive graph node representations, and then contrastive learning based on data augmentation was introduced for graph domain alignment, which not only extracted semantic information within a single domain but also promoted more sufficient knowledge transfer between domains. Experimental evaluation results  on Citation network datasets show  that the proposed method can transfer rich labeled knowledge from the source graph domain to the unlabeled target graph domain, solve the reliance on labels for graph representation learning, reduce the cost of  manual annotation, and outperform the  graph domain adaptation classical algorithms.

Aiming at  the limitations of existing research on respiratory rate prediction  in deep joint analysis of multimodal physiological signals, as well as the challenge of balancing long-term temporal dependencies and capturing local details, we  proposed a prediction model based on a dynamic multidimensional feature fusion network. Firstly, we constructed an adaptive multi-scale fusion module to dynamically extract multi-frequency features from both electrocardiogram and photoplethysmography, respectively, to generate a single-modal feature map containing rich  multi-scale information, thereby resolving the problem of limited receptive field of a single convolutional kernel.   Secondly, the model incorporated a hybrid spatio-temporal attention mechanism. By stacking Transformer encoding blocks and integrating local, global, and spatio-temporal triple attention strategies, 
it achieved deep interaction between heterogeneous features and precise modeling of long-term temporal dependencies. Validation results based on the BIDMC and CapnoBase public datasets show  that the mean absolute errors of the model reach 1.08 beats/min and 0.76 beats/min, respectively, which is  significantly better than  existing mainstream models in terms of accuracy 
and robustness, and can provide theoretical basis  for clinical non-invasive health monitoring.

Aiming at  the problem of imbalance between recognition accuracy  and network  structure complexity, we proposed  a lightweight identification model Weed-YOLO for corn seedling weed based on improved YOLOv9. Firstly, FasterNet module was introduced as the backbone network of YOLOv9 model to effectively reduce the complexity of the model. Secondly, the bidirectional feature pyramid network was used to replace original path aggregation network and feature pyramid network modules to integrate 
multi-scale weed features, compensate for the decrease in recognition accuracy caused by lightweight backbone networks, and further reduce the complexity of the model. Finally, Inner_CIoU loss function was used to calculate the boundary frame loss, which improved the convergence speed and overall performance of the model. The experimental results show  that the accuracy, recall rate and mean precision of Weed-YOLO model in identifying corn seedling weeds are  94.1%, 95.9% and  97.6%, respectively.  The parameter count, amount of calculation and model size decrease by 39.15%,44.79% and 39.18%, respectively. It can accurately distinguish  weeds and crops, and reduce  resource utilization of the model.

Aiming at  the problem of unclear  small-target features and insufficient detection accuracy in the defect detection task of industrial printed circuit boards, we proposed an improved  algorithm based on YOLOv8 algorithm. Firstly, we  adapted  the defect detection of printed circuit boards by adding or deleting the feature map sizes, and drew on the experience of  the weighted bi-directional feature pyramid network structure to retain the features of the original image. Secondly, we designed a lightweight module at the neck  for feature extraction by using group convolution, which  improved the detection accuracy while reducing the complexity of the model. Finally, before the  small-object detection head, we introduced coordinate attention module that could  enhance feature representation capabilities, further improving the inspection accuracy. The experimental results show that the improved algorithm can improve the detection accuracy  mAP@0.5 to  95.4% and achieve a detection speed FPS (frames per second) of 105.4, which  can better  meet the  requirements of industrial detection for accuracy and real-time performance.

Aiming at the problem of the complex  harmonic components in the current harmonic measurement of electronic current transformers, which  led to interference from noise and outliers in actual measurement, resulting in a decrease in the accuracy of harmonic measurement results. By introducing DBSCAN (density-based spatial clustering of applications with noise) clustering, we proposed a harmonic measurement algorithm for electronic current transformers based on DBSCAN clustering to effectively identify and eliminate noise points and outliers in the dataset, thereby improving the accuracy of harmonic component detection. Firstly, we collected the current signals of the electronic current transformer and obtained the peak frequency of each current signal in 
the transformer based on the time-frequency energy peak value. Secondly, by using the DBSCAN clustering algorithm, we calculated the distance between the peak frequencies of each current signal, and determined noise signals, non harmonic signals, and different types of harmonic signals based on the distance to eliminate noise points and outliers in the dataset. Finally, we  used the least squares method to measure the amplitude and phase of various harmonic signals, and obtained the harmonic measurement results of the current transformer. The experimental results show that when the time is 2 s, the actual value of harmonic phase is 18°, and the harmonic phase of the proposed algorithm is 18°, which is consistent with the actual results. The measurement  accuracy of harmonic  amplitude and phase is high,  indicating that the proposed algorithm  can effectively improve the accuracy of harmonic measurement and avoid interference from noise and outliers.

Aiming at  the limitations of the original density peaks clustering algorithm, including its neglect of inter-cluster density variations, requirement for predefining the number of clusters, and reliance on a single allocation strategy, we proposed a density peak clustering algorithm based on adaptive hierarchical shared neighbors. Firstly, we  calculated similarity between samples and redefined local density and relative distance by adaptively sharing  neighbors and hierarchically increasing  weights. Secondly, we introduced the second-order derivatives to identify inflection points and calculated the weighted triangular areas based on inflection point information to automatically select clustering centers. Finally,  we combined the similarity matrix with relative distance for  secondary allocation to reduce the effects of  chain reactions. Experimental results on nine artificial datasets and nine UCI real datasets show that the proposed algorithm generally outperforms the density peaks clustering algorithm and other improved algorithms in clustering performance, exhibiting higher accuracy and robustness, and is well-suited for clustering analysis of complex data distributions.

Aiming at the problem that there was no obvious space separation between words in Chinese, which led to unclear vocabulary  boundaries, and it was difficult to accurately capture the relationship between entities and surrounding words, resulting in low  accuracy of Chinese named entity recognition, we proposed  a  fine-tuning optimization method of Chinese named entity 
recognition based on XLM-RoBERTa-Large-Finetuned-Conll03-English model combined with conditional random field (CRF). Firstly, we  established a Chinese named entity indicator lexicon, determined the scope of named entities,  sorted the entities, and used probability calculation to obtain the optimal features of named entities. Secondly, we introduced the features obtained by CRF into the XLM-RoBERTa-Large-Finetuned-Conll03-English model to capture the feature sequences of named entities and their dependencies. Finally, by adding CRF layer to the multi-language model, the fine-tuning optimization of Chinese named entity recognition was realized. The experimental results show that this fine-tuning optimization method significantly improves the performance of Chinese named entity recognition, enabling the model to have higher accuracy and lower loss value, and  better applicability in Chinese named entity recognition (NER) task.

Aiming at  the problem of texture detail loss in common  image enhancement techniques when improving the contrast of low-quality images, we proposed a low-quality image enhancement method based on dynamical system by constructing a four-dimensional feedforward neural network model and optimizing the output function. Firstly, through the analysis of the dynamical characteristics of the neural network model, we studied the  parameter combinations that achieved optimal signal amplification effects. Secondly, comparative experiments with mainstream enhancement algorithms were conducted on high-complexity medical image datasets. The results show that this method can enhance low-quality images with problems such as detail loss, brightness reduction, and noise contamination into high-quality images, and is  suitable for medical image enhancement processing with stringent quality requirements. The proposed method  provides a new technical approach for fields with strict quality requirements, such as medical images, effectively balancing image contrast enhancement and detail preservation, and  improving the usability of low-quality images in practical applications such as clinical diagnosis.

Aiming at the problem that  the efficiency and performance of image object recognition algorithms on embedded systems were limited due to the small processing speed and memory size of embedded systems, we proposed a high-performance embedded image object recognition algorithm that combined convolutional neural network (CNN) and non negative sparse representation. Firstly, by utilizing CNN to mine embedded image features, parameter sharing and local perception could reduce the model’s parameter count and computational complexity, thereby  improving computational efficiency. Secondly, convolution operation was performed on embedded images by using Roberts cross gradient filter, preliminary feature mining results were obtained by  combining the Sigmoid function operation, and then the non-linear pooling method was used to downsample the results, thereby reducing the dimensionality of feature mining results and completing the image feature mining task. Finally, we used non negative sparse representation to establish a target recognition model, and  solved the coefficient sparse coefficient vector based on 
multiplicative iterative algorithm.  The target area was  determined through kernel function operation and minimum class residue operation. The experimental results show that the F₁ values of each group of image recognition results obtained by the proposed method are stable above 0.98, and the frame rate is high in embedded image target recognition, indicating that the method has the ability to run efficiently on embedded systems while maintaining high-precision recognition performance.

Aiming at the problem of  the low accuracy of speech keyword spotting under low-resource conditions, we proposed a detection method combining unsupervised feature extraction and supervised model parameter transfer. Firstly, a deep feature extraction network was trained by using large-scale unlabeled speech data, and the extracted features were fused with acoustic spectrogram 
features to enhance robustness of the features to  acoustic environments. Secondly, the decision network was pre-trained by using rich labeled data from the source domain, and decision knowledge was introduced through parameter transfer to solve the problem of model convergence difficulty caused by insufficient training data in the target domain. Finally, the entire network was fine-tuned by using  a very small amount of target domain data. Experimental results on Hakka and Cantonese datasets show that this method significantly outperforms single transfer strategies. In the Hakka task, the false rejection rate is reduced to 11.77%, and the maximum term weighted  value is improved to 0.734 6. The experimental results demonstrate that the proposed method can effectively alleviate the problem of data scarcity and significantly improve detection performance for low-resource languages.

Aiming at  the problem of susceptibility to outlier interference and unstable optimization during training process of  multi-index speech enhancement algorithms, we proposed an adaptive speech enhancement algorithm based on a multi-head attention mechanism. Firstly, by  introducing a multi-head attention structure into the intermediate layer of the discriminator network, we  enhanced the joint modeling ability of the  model for local features and overall structure of speech spectrum, and  combined it with an online knowledge distillation strategy to achieve information sharing among multiple generators, thereby improving the collaborative optimization effect under multi-index conditions. Secondly, in order to reduce the impact of outliers on the training process, we replaced the loss function with a logarithmic mean-squared error form to improve  stability and robustness of the model. Experimental results on the publicly available speech dataset VoiceBank-DEMAND show that this method outperforms existing multi-index speech enhancement models in terms of speech quality, background noise suppression, and speech intelligibility metrics. Therefore,  introducing an attention mechanism and a stabilizing loss function can significantly improve the overall performance of multi-index speech enhancement algorithms.

Aiming at the problem that the communication interruptions between vehicles and base stations was not fully considered in current vehicular networks with edge computing, and  the resource wastage caused by offloading tasks to a single node for computing, we proposed a vehicular network resource optimization scheme based on the simulated annealing algorithm (SAA). Taking into account the communication retention time and task offloading computation efficiency, we modelled the problem of minimizing the system utility by balancing system latency and energy consumption, and then decomposed it into subproblems of resource allocation and task offloading ratio optimization to solve. Firstly, the resource allocation subproblem was solved by using the Lagrange multiplier method and quasi-convex optimization techniques. Secondly, the SAA was used to jointly optimize the task offloading ratio and resource allocation subproblems. Simulation experiment results show that the proposed scheme can effectively reduce  average latency, energy consumption, and utility of the system, and has good convergence, which  can solve  the problems of latency sensitivity, high energy consumption, and high system overhead in vehicular networks for various applications.

Aiming at  the information security problems  caused by the broadcast characteristics in  wireless communications, we proposed a secrecy rate maximization algorithm based on alternating iteration. Firstly, considering non-ideal channel conditions, we modelled the secrecy rate maximization problem for an active reconfigurable intelligent surface (RIS)-assisted  multiple-input single-output (MISO) system with multiple eavesdroppers in the downlink. Secondly, aiming at the non-convexity and coupling of the optimization problem, we transformed the original non-convexity problem into two subproblems and  optimized  beamforming vector and the active RIS phase shift matrix of the base station separately. Finally, we used the alternating iteration and  the minimization-maximization (MM) algorithms  to transform the subproblems into convex optimization problems for solving. Simulation experiment results show  that compared with traditional schemes, the proposed algorithm improves the secrecy performance by 10%—35%, significantly enhances the system security performance and has  strong robustness, providing an effective and robust new method for solving wireless communication security problems in complex channel environments.

We studied the bifurcation behaviors of equilibrium points and limit cycles as well as attraction domain of equilibrium state of a modified wing model. The results show that bifurcation structure of equilibrium state is affected by the coefficients of the structural restoring moment so that two pairs of nontrivial equilibrium points with opposite stability coexist or vanish due to the simultaneous occurrence of Fold bifurcations. The attraction domains exhibit a centrosymmetric structural distribution when some initial components are fixed. When the frequency ratio is used as a bifurcation parameter, the trivial equilibrium point loses stability due to Hopf bifurcation, and the stable limit cycles undergo a Pitchfork bifurcation to produce two stable limit cycles. With further reduction of the frequency ratio, two coexisting limit cycles simultaneously undergo a Neimmark-Sacker bifurca
tion, leading to two stable two-dimensional toruses.

We proposed a new evaluation scheme and standard for the total absorption Gamma ray spectroscopy data of the 70 important short-lived nuclei, combined with direct measurement data for systematic comparison and evaluation, and conducted theoretical research on β decay based on the Gross theory. The research results show the inaccurate description of high-energy density and transition probability caused by odd nucleon is currently the main factor affecting the physics description of decay heat.

The control problem of a class of Hamiltonian systems with parameter coupling was studied. Firstly, the complex dynamic behavior of the system under certain parameters was verified by drawing Lyapunov exponent diagram, chaotic attractor diagram and time domain waveform diagram. Secondly, sliding mode control method, adaptive backstepping control method and high frequency robust control method were used to design the controller, and the state of the chaotic system was stabilized to the equilibrium point. Finally, the effectiveness of the designed controller was verified by numerical simulation of MATLAB software, and its control effect was compared.

Aiming at the problem that the small molecule uric acid lacked immunogenicity and it was difficult to directly detect it using immunological methods, we modified uric acid with succinic anhydride to obtain a modified uric acid hapten, and then conjugated the uric acid hapten with bovine serum albumin and ovalbumin to prepare uric acid artificial antigens and coating antigens. We immunized mice with uric acid artificial antigens to prepare uric acid polyclonal antibodies. Uric acid hapten was characterized by Fourier transform infrared spectroscopy and mass spectrometry, artificial antigen and coating antigen were characterized by ultraviolet spectrophotometry and polyacrylamide gel electrophoresis, and antibody titer, sensitivity and specificity were determined by indirect competitive enzyme-linked immunosorbent assay (ELISA). The results show that the titers of the multi antibody serum are all above 1∶25 600, and the sensitivities of the antibodies in mice 1—4 are 10.337,8.426,16.457,21.177 μg/mL, respectively. The cross reactivity rates between the antibodies and structural analogues of uric acid are all less than 1%. It can be seen that the uric acid polyclonal antibody prepared by immunization in this experiment has achieved high potency, high sensitivity, and strong specificity, providing experimental basis for the immunological detection of uric acid. 

In order to reveal the response mechanism of microbial communities to pH values, we collected natural pH gradient soil, characterized their physicochemical properties, analyzed the structure and composition of the bacterial communities, and identified key factors that caused differences of bacterial community structure and composition in different environments. The results show that soil pH value is negatively correlated with the relative abundance of Proteobacteria and Acidobacteria (p<0．01), and positively correlated with the relative abundance of Actinobacteria (p<0．01). There are many nodes and links of the bacterial community network in neutral and weakly alkaline soils with higher moduarity. In weakly acidic and strongly alkaline soils, there are fewer links in the bacterial community network, resulting in a lower degree of modularity. The bacterial community is directly or indirectly influenced by soil physicochemical properties.  The distribution of bacterial communities is mainly determined by soil pH value, electrical conductivity (EC), and water-soluble organic carbon (WSOC) content. Among them, soil pH value is the main environmental variable affecting bacterial communities in soils. The research results reveal the mechanism by which pH value affects soil bacterial communities, which is of great significance for a deeper understanding of soil microecology, and provides useful information for the design of land use and soil management strategies. 

In order to improve the degradation rate of  norfloxacin residues in the environment, we prepared a rice husk biochar based graphite phase nitrogen doped carbon (g-C₃N₄) composite photocatalyst through a one-step calcination method. We characterized its structure by using various methods, substituting the bridging nitrogen atoms in the g-C₃N₄ lattice with carbon atoms to effectively construct a delocalized π-bond system, significantly enhancing its photocatalytic degradation performance of norfloxacin. Experimental results show  that the photocatalytic degradation rate constant of the optimized biochar g-C₃N₄ composite photocatalyst can reach up to  0.029 4 min^-1, and the degradation rate of norfloxacin can be increased to 85.45% within 2 h, which is 1.46 times  that of pure g-C₃N₄ material. This article provides novel design concept for developing highly efficient and stable photocatalysts for water treatment, demonstrating the application potential of biochar g-C₃N₄ composite materials  in the field of environmental remediation.